What is the smallest possible answer for X? X is a whole number.

SOLUTION

From the question, we have that

so for

Hence

Also for

Hence

Finally, we have that

Hence we have that

Hence

Answer:

14322 * 10¹²

1.4322 * 10¹⁶

Step-by-step explanation:

14322000000000000

14322 * 10¹²

1.4322 * 10¹⁶

Answer:

823543

Step-by-step explanation:

\(7^3\cdot \:7^6\cdot \:7^{-2}\)

\(\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\)

\(7^3\cdot \:7^6\cdot \:7^{-2}=7^{3+6-2}\)

\(=7^{3+6-2}\)

\(\mathrm{Add/Subtract\:the\:numbers:}\:3+6-2=7\)

\(=7^7\)

\(7^7=823543\)

Answer = 823543

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There are 2 pigeons jumped down to the street.

Total no. of pigeons on a curb=9

No. of pigeons fly away=3

No. of pigeons stayed in the curb=4

Thus, the total number of pigeon that jumped down to the street is 9 - 3 - 4 = 2

This exemplifies the pigeonhole principle, which asserts that if there are more pigeons than there are pigeonholes, then there must be at least one pigeonhole with at least two pigeons in it. II) We can state that at least one box contains two or more objects if n + 1 things are placed within n boxes.

Hence, there are 2 pigeons jumped down to the street.

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There are 2 pigeons jumped down to the street.

Total no. of pigeons on a curb=9

No. of pigeons fly away=3

No. of pigeons stayed in the curb=4

Thus, the total number of pigeon that jumped down to the street is 9 - 3 - 4 = 2

This exemplifies the pigeonhole principle, which asserts that if there are more pigeons than there are pigeonholes, then there must be at least one pigeonhole with at least two pigeons in it. II) We can state that at least one box contains two or more objects if n + 1 things are placed within n boxes.

Hence, there are 2 pigeons jumped down to the street.

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The function of  f(x) = (x+4)³ + 3 is one-to-one  then the value of

\(f^{-1} (x) = \sqrt[3]{x} - 4\) and,

\(f^{-1} (2) = -2.7401\)

The function f(x) = (x+4)³ + 3

Let us assume,

y = (x+4)³ + 3

A function is said to be invertible when it has an inverse. It is represented by \(f^{-1}\). Condition for a function to have a well-defined inverse is that it be one-to-one and Onto or simply bijective.

Then,

y = (x+4)³   and    y = 3

Therefore the inverse of y = 3 is the line x = 3

We can solve,

y = (x+4)³

The solution of Inverse function,

So,

\(\sqrt[3]{y} = x+4\)

We can get,

\(x = \sqrt[3]{y} -4\)

So the inverse of y is \(\sqrt[3]{x} -4\)

f(x) = (x+4)³

So the inverse of f(x) is \(\sqrt[3]{x} -4\)

Therefore, \(f^{-1}( x)\) = \(\sqrt[3]{x} -4\)

Then f(x) = 2

\(f^{-1} (x) = \sqrt[3]{x} - 4\)

We can substitute f(x) = 2

\(f^{-1} (2) = \sqrt[3]{2} -4\)      

Since, ∛2 = 1.2599

We can substitute this value,

\(f^{-1} (2) = 1.2599-4\)

\(f^{-1} (2) = -2.7401\)

Therefore,

The value of ,

\(f^{-1} (x) = \sqrt[3]{x} - 4\) and,

\(f^{-1} (2) = -2.7401\)

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Answer:

Answer down below

Step-by-step explanation:

h (3x-4)

= \(\frac{1}{3x-4+2}\)

= \(\frac{1}{3x-2}\)

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:

Step-by-step explanation:

Hope it helps!!

Triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1): 90° counterclockwise transformation is A'(-7, 2), B'(-5, 6) and C'(-1, 4).

Given that, triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1).

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

90° counterclockwise rotation: (x, y) becomes (-y, x)

A(2, 7) → A'(-7, 2)

B(6, 5) → B'(-5, 6)

C(4, 1) → C'(-1, 4)

Therefore, triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1): 90° counterclockwise transformation is A'(-7, 2), B'(-5, 6) and C'(-1, 4).

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The solution to the linear system is c = -6 and d = 3.

To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:

(1) 12c + 28d = 12

(2) -20c + 16d = 168

To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:

(1) 60c + 140d = 60

(2) -60c + 48d = 504

Now, we can add the equations:

(60c + 140d) + (-60c + 48d) = 60 + 504

188d = 564

d = 564/188

d = 3

Substituting the value of 'd' back into equation (1):

12c + 28(3) = 12

12c + 84 = 12

12c = 12 - 84

12c = -72

c = -72/12

c = -6

The solution to the linear system is c = -6 and d = 3.

Now let's analyze the second linear system:

(1) 7x - 3y = 43

(2) 7x - 3y = 13

By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.

The linear system has no solution.

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Option D, which is the closest choice to 933.33, is 930. As a result, 930 fraction acres is a plausible estimate of the amount of acres on which Mr. Bailey will plant soybeans

A fraction is a number that represents a portion of a whole or a ratio between two quantities in mathematics. It is represented as a top number (numerator) over a bottom number (denominator) divided by a horizontal line, also known as a vinculum. The fraction 3/4, for example, represents three-quarters of a whole that has been divided into four equal parts. Proper fractions, improper fractions, and mixed numbers are all ways to express a fraction. A suitable fraction is one in which the numerator is less than the denominator, for example, 2/5.

Mr. Bailey intends to plant soybeans on 4 of every 9 acres, which equates to (4/9) of the total acres he farms.

If he intends to cultivate 2,100 acres, the number of acres planted with soybeans is:

(4/9) x 2,100 = 933.33

We must round this amount to the next whole number because he cannot plant soybeans on a fraction of an acre.

Option D, which is the closest choice to 933.33, is 930. As a result, 930 acres is a plausible estimate of the amount of acres on which Mr. Bailey will plant soybeans.

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Answer:

I believe that it is (2,4)

Step-by-step explanation:

f(2) would be your y

4 would be your x

to write a point on a graph you wright (x,y)

(2,4)

The correct representation of function f(2) = 4 in coordinate form (x,y) is (2,4)

What is Mathematical function ?

Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.

In other words the function represents the graph between x and y that is for each value of x there exist one value of y but here there is no restriction in values of y that is y can have infinity values.

Here, the given function is f(2)=4

which implies that the independent variable is x=2 which gives the value after substituting in the function gives value y=4.

Therefore,The correct representation of function f(2) = 4 in coordinate form (x,y) is (2,4)

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Answer:

10. x ≈ 15,9

11. x ≈ 17,5

Step-by-step explanation:

10. Use the Pythagorean theorem:

\( {x}^{2} = {17}^{2} - {6}^{2} = 289 - 36 = 253\)

\(x > 0\)

\(x = \sqrt{253} ≈15.9\)

11.

\( {x}^{2} = {9}^{2} + {15}^{2} = 81 + 225 = 306\)

\(x > 0\)

\(x = \sqrt{306} ≈17.5\)

Answer:

The length of DE is 7.2 units.

Explanation:

In the figure:

Triangles CBA and AGE are similar, thus:

Thus, we have that:

The length of DE is 7.2 units.

On solving the provided question, we can say that - the range \(|x + 1| = 0\) \(x + 1 = 0 = > x = -1\) and \(y = 3\)

Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.

The regions where the absolute values are zero are known as the vertex points of an absolute value function.

\(|x + 1| = 0\\x + 1 = 0\\x = -1\)

\(y = |-1 + 1| + 3\\y= 0 + 3\\y = 3\)

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Algebraic expression for the number of pounds of cashews that she needs to add is c = 58 - p

An algebraic expression can be described as an expression that is mostly composed or consists of variables, coefficients, terms, factors and constants.

Algebraic expressions are mathematically expressions and thus are made up of arithmetic operations, such as;

From the information given, we have that;

To determine the number of pounds of cashew, we have;

p + c = 58

Make 'c' the subject

c = 58 - p

Hence, the expression is c = 58 - p

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The possible roots of the cubic polynomial 9x³ + 14x² - x + 18 are 1, 2, and 3.

The rational root theorem explains how a polynomial's roots and coefficients are related. It explains the kind of rational roots that the polynomial might have in particular.

According to the rational root theorem, the possible roots of a polynomial of degree three and above are,

± (coefficient of the last term)/(coefficient of the first terms).

Given, A polynomial 9x³ + 14x² - x + 18 it is a cubic polynomial so it should have three roots they could be,

The factors of the constant term divided by the factors of the first terms,

So, 18 has factors ± (1, 2, 3, 6, 9, 18) and 9 has factors ± (1, 3, 9).

So, The possible roots are ± (1, 2, 3) and so on.

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Answer:

You would need 2.44 seconds per drink.

Step-by-step explanation:

This question can be solved using proportions.

A month has 30 days, each with 24 hours, each with 3600 seconds.

So a month will have 30*24*3600 = 2,592,000 seconds.

It can provide 1,063,953 fountain drink and slush combinations.

So, the number of seconds per drinks is given by:

2592000/1063953 = 2.44

You would need 2.44 seconds per drink.

The first cellphone service provider to be established in South Africa was Vodacom. Vodacom was launched on April 1, 1994, and it became the country's first cellular network operator.

The company was a joint venture between Telkom, the national telecommunications company of South Africa, and Vodafone, a global telecommunications giant.

Vodacom introduced the GSM network to South Africa, providing mobile voice and data services to customers across the country. Its launch marked a significant milestone in the telecommunications industry in South Africa, as it brought mobile communication to the masses and revolutionized the way people connect and communicate.

Since its inception, Vodacom has played a pivotal role in the development of the telecommunications sector in South Africa. It has continually expanded its network coverage, introduced innovative services, and played an active role in bridging the digital divide in the country.

Today, Vodacom remains one of the leading mobile network operators in South Africa, providing a wide range of mobile services to millions of customers.

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The probable question may be:

Which cellphone service provider was the first to be established in south africa

Answer:

37

Step-by-step explanation:

(6 × 5) + (10 - 3)

30 + 7

37

Answer:

A.

Step-by-step explanation:

answer A. 14 minutes is your answer

three shapes. three areas to find. three areas to add together to find the whole area. gotcha.

Step-by-step explanation:

length is 7 cm and width is 4 cm, so the area is 28 square cm

width is 4 cm and length is 10 cm, so the area is 40 square cm

Because the weird shape's bottom length was 13 cm. There are 3 cm and 7 cm on the top length(s) of the weird shape, next to each other. Looking at the dash lines, when adding 3 cm and 7 cm together, the larger rectangle's length is 10 cm.

base is 3 cm and height is 8 cm, so the area is (3x8)/2 = 24/2 = 12 square cm

With knowledge from figuring out the larger rectangle's length being 10 cm and the weird shape's bottom length being 13 cm, we know the right triangle's base is 3 cm. (13 cm - 10 cm = 3 cm for the base of the right triangle).

Due to adding 4 cm and 4 cm of weird shape's width, which is also a right triangle's height.

28 + 40 + 12

= 80 square cm (ANSWER)

Answer:

A polygon is a pentagon if and only if it has five sides."If this statement is true, then which of the follow… Get the ... The given statement is of the form

Step-by-step explanation:

hope it helps you

❤❤❤❤❤

Answer:

D.  If it is a pentagon, then it has five sides. If the polygon has five sides, then it is a pentagon

Step-by-step explanation:

Given statements;

      A polygon is a pentagon if and only if it has five sides.

Therefore, this bi-conditional statement is premised on two "if"s,

    If it is a pentagon then we are dealing with a body with 5 sides.

   And if such body has five sides, it is a polygon called pentagon

The correct option is D

Choice A, B and C are logically flawed.

A.  If it is a pentagon, then it has five sides. If it is a polygon, then it is a pentagon.

The emboldened part we do not know.

B.  If it is a pentagon, then it is a polygon. If it is a polygon, then it is a pentagon

 The emboldened part is flawed.

C. If it is a pentagon, then it is a polygon. If it is a polygon, then it has five sides.

We do not know if all pentagons have 5 sides.

The answers are 4. a) 15.7 cm, b) 26.25 m, 5. a) 128.74 cm, b) 40.82 mm, c) 45 cm and 6. 777.28 cm

Given are the circles and the circular items we need to find their circumference,

Circumference of a circle = 2π × radius = Diameter × π

4. a) Circumference = 5 × 3.14 = 15.7 cm

b) Circumference = 8.36 × 3.14 = 26.25 m

5. a) Circumference = 41 × 3.14 = 128.74 cm

b) Circumference = 13 × 3.14 = 40.82 mm

c) Circumference = 14.3 × 3.14 = 45 cm

6.

The perimeter of the cloth = circumference of the circular ends plus length in the middle,

= 76 × 2 × 3.14 + 150 × 2

= 477.28 + 300

= 777.28 cm

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Step-by-step explanation:

This is the second fundamental theorem of calculus.

d/dx ∫ₐᵇ f(x) dx = f(b) (db/dx) − f(a) (da/dx)

This is derived using chain rule:

d/dx g(f(x)) = g'(f(x)) f'(x)

Therefore:

d/dx ∫₀²ˣ arctan(t) dt = arctan(2x) (2x)' = 2 arctan(2x)

Answer: The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Step-by-step explanation: irst, we calculate the amount of discount that is applied to the original price:

30% of $1199 = 0.3 x 1199 = $359.70

So, the discounted price is:

$1199 - $359.70 = $839.30

Next, we apply the additional 10% off coupon to this discounted price:

10% of $839.30 = 0.1 x $839.30 = $83.93

The final price after the coupon is applied is:

$839.30 - $83.93 = $755.37

Finally, we calculate the sales tax on this final price:

7% of $755.37 = 0.07 x $755.37 = $52.88

The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Nine pears in all are contained in the little basket. Based on distributive law, it operates.

The distributive law, which states that equality is always true in elementary algebra, is generalized by the distributive principle of binary operations in mathematics.. For instance, in basic mathematics, one has to One claims that addition distributes more evenly than multiplication.

According to the Distributive Law, multiplying a number by a collection of numbers is equivalent to performing each multiplication independently. Example: 3 × (2 + 4) = 3×2 + 3×4.

According to the information provided,

apple = 6

orange =5

pear=3

to add whole item;

6+5+3

=14

the no. of pears =total pieces of fruit in basket / total fruit

                      =42/14

                      =3

the no of pears = 3*3=9  

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Answer:

No

Step-by-step explanation:

Answer:

you see

Step-by-step explanation: